Four-quark structure of Zc(3900), Z(4430) and Xb(5568) states

We examine the four-quark structure of the recently discovered charged $Z_c(3900)$, $Z(4430)$, and $X_b(5568)$ states. We calculate the widths of the strong decays $Z_c^{+}\to J\mathrm{/}\psi {\pi }^{+}$ (${\eta }_c{\rho }^{+}$, ${\bar{D}}^0{D}^{\ast +}$, ${\bar{D}}^{\ast 0}{D}^{+}$), $Z(4430{)}^{+}\to J\mathrm{/}\psi {\pi }^{+}$ ($\psi (2s){\pi }^{+}$), and $X_b^{+}\to B_s{\pi }^{+}$ within a covariant quark model previously developed by us. We find that the tetraquark-type current widely used in the literature for the $Z_c(3900)$ leads to a significant suppression of the $\bar{D}{D}^{\ast }$ and $\bar D^\ast D$ modes. Contrary to this a molecular-type current provides an enhancement by a factor of 6-7 for the $\bar{D}{D}^{\ast }$ modes compared with the $Z_c^{+}\to J\mathrm{/}\psi {\pi }^{+}$, ${\eta }_c{\rho }^{+}$ modes in agreement with recent experimental data from the BESIII Collaboration. In case of the $Z(4430)$ state we test a sensitivity of the ratio $R_Z$ of the $Z(4430{)}^{+}\to \psi (2s){\pi }^{+}$ and $Z(4430{)}^{+}\to J\mathrm{/}\psi {\pi }^{+}$ decay rates to a choice of the size parameter ${\mathrm{\Lambda }}_{Z(4430)}$ of the $Z(4430)$. Using upper constraint for the sum of these two modes deduced from the LHCb Collaboration data we find that $R_Z$ varies from 4.64 to 4.08 when ${\mathrm{\Lambda }}_{Z(4430)}$ changes from 2.2 to 3.2 GeV. Also we make the prediction for the $Z(4430)^+ \to D^{\ast,+} \bar D^{\ast,0}$ decay rate.